A Note on the Existence of Equilibria in Incomplete Markets with Non-Ordered Preferences

We consider a two-period exchange economy with a finite set of con-sumers, states of nature, independent assets and a single consumption good. We prove the existence of competitive equilibrium in incomplete markets, when consumption set is not assumed to be compact, set of assets is linearly independent, and individuals ’ preferences are not assumed to be complete or transitive. Our study therefore generalises various results in the existing literature